uiz 3 Statistics 200 - October 2015 There are again 5 problems on this quiz. Again, it is not meant to be tricky or hard, but to ensure you are comfortable with the concepts in the assigned chapters. Please submit your quiz to your assignment folder. If you have issues submitting, please do not use email. Submit with your homework assignment and I will pick it up there. It has to be submitted into LEO for credit. Answer key will be posted on Tuesday. ______________________________________________________ Problem 1 Below are five (5) separate distributions. a- Calculate the Range b- Use the range to calculate the standard deviation c- Calculate the standard deviation (and show any difference) Problem 2 Two (2) students took the same statistics test. Convert their scores to percentiles and plot on a chart. You will need the z-table in the back of the text (or internet search). Math Test Results X = 73.0 s = 8.0 John scores 79 on the test Mary scored 68 on the test Problem 3 I have finished analyzing the data from a recent study. There are 25 subjects in the sample The mean of the sample is 75 The standard deviation is 4.7 Please answer the following: a- What is the standard error o the mean for these data? b- What are the 95% and 99% confidence intervals c- What is the probability of obtaining by chance the following: i - a mean less than 72 ii- a mean less than 74 iii- a mean greater than 76 iv- a mean greater than 78 Problem 4 Use the following information to write the corresponding null and alternative hypothesis: a- A sample mean of 23 is statistically different from a population mean of 30 b- A sample mean of 56 is less than the population mean of 70 c- A sample mean of 75 is greater than the population mean of 70 Be sure to show the relationship! Not just words. Problem 5 I am back in the lab, collecting samples. The mean of the sample is 75 My associate wants to determine whether the sample mean statistically greater than the population mean of 70. My associate set = 0.05 Please provide responses to: a- The probability associated with a mean of 75 is p = 0.05Can my associate reject the null hypothesis? b- If the null hypothesis is a correct statement, what is the probability that the researcher will make the correct decision not to reject the null hypothesis? Quiz 3 Statistics 200 - October 2015 There are again 5 problems on this quiz. Again, it is not meant to be tricky or hard, but to ensure you are comfortable with the concepts in the assigned chapters. Please submit your quiz to your assignment folder. If you have issues submitting, please do not use email. Submit with your homework assignment and I will pick it up there. It has to be submitted into LEO for credit. Answer key will be posted on Tuesday. ______________________________________________________ Problem 1 Below are five (5) separate distributions. a- Calculate the Range b- Use the range to calculate the standard deviation c- Calculate the standard deviation (and show any difference) a) Range = Max - Min b) Using the range rule of thumb, the relation between range and standard deviation, Range 4 c) The actual formula for standard deviation, 1 n 1 x x 2 The following table gives the necessary values for each distribution as follows: 1 6 5 4 4 4 4 4 3 2 x max min range standard deviatio stdev 3 6 6 5 5 4 3 3 2 2 4 6 6 6 5 4 3 2 2 2 5 6 6 6 6 4 2 2 2 2 37 x 2 6 5 5 4 4 4 3 3 2 38 39 40 41 154 156 164 170 176 2 6 2 4 6 2 4 6 2 4 6 2 4 6 2 4 1 1 1 1 1 1.11803 4 1.22474 5 1.58113 9 1.80277 6 2 Problem 2 Two (2) students took the same statistics test. Convert their scores to percentiles and plot on a chart. You will need the z-table in the back of the text (or internet search). Math Test Results X = 73.0 s = 8.0 John scores 79 on the test Mary scored 68 on the test The Z-score is defined as Given that X 8 Then, the Z-score for John score, ZJ 79 73 6 0.75 8 8 The Z score is 0.75 and the corresponding percentile, The corresponding chart is shown as follows: P Z 0.75 0.7734 77.34% Given that 8 Then, the Z-score for John score, ZM 68 73 5 0.625 8 8 The Z score is -0.625 and the corresponding percentile, The corresponding chart is shown as follows: P Z 0.624 0.266 26.6% Problem 3 I have finished analyzing the data from a recent study. There are 25 subjects in the sample The mean of the sample is 75 The standard deviation is 4.7 Please answer the following: a- What is the standard error o the mean for these data? b- What are the 95% and 99% confidence intervals c- What is the probability of obtaining by chance the following: i - a mean less than 72 ii- a mean less than 74 iii- a mean greater than 76 iv- a mean greater than 78 Answer: Given that n 25, x 75, s 4.7 a)The standard error of the mean, x b) The 1 % s 4.7 0.94 n 25 confidence interval for the mean is defined by x t s n The 95% critical value of 't' at 25-1=24DF is 2.064. Then, the 95% confidence interval for the mean is given by x t s 4.7 75 2.064 n 25 75 1.94 23.06, 26.94 The 99% critical value of 't' at 25-1=24DF is 2.064. Then, the 95% confidence interval for the mean is given by x t s 4.7 75 2.7969 n 25 75 2.629 22.3709, 27.6291 c) 72 75 x s n 4.7 / 25 P x 72 P P t24 3.1915 0.00196 Using excel function =tdist 3.1915, 24,1 74 75 x s n 4.7 / 25 P x 74 P P t24 1.0638 0.14899 Using excel function =tdist 1.0638, 24,1 76 75 x s n 4.7 / 25 P x 76 P P t24 1.0638 1 P t 24 1.0638 1 0.14899 Using excel function =tdist 1.0638, 24,1 0.8563 78 75 x s n 4.7 / 25 P x 78 P P t24 3.1915 1 P t 24 3.1915 1 0.00196 Using excel function =tdist 1.0638, 24,1 0.998 Problem 4 Use the following information to write the correspondingnull and alternative hypothesis: a- A sample mean of 23 is statistically different from a population mean of 30 Null hypothesis: The mean is same as population mean Alternative hypothesis: The mean is not the same as population mean b- A sample mean of 56 is less than the population mean of 70 Null hypothesis: The mean is not less than population mean 70 Alternative hypothesis: The mean is less than population mean c- A sample mean of 75 is greater than the population mean of 70 Null hypothesis: The mean is not greater than population mean 70 Alternative hypothesis: The mean is greater than population mean Problem 5 I am back in the lab, collecting samples. The mean of the sample is 75 My associate wants to determine whether the sample meanstatistically greater than the population mean of 70. My associate set = 0.05 Please provide responses to: a- The probability associated with a mean of 75 is p = 0.05Can my associate reject the null hypothesis? b- If the null hypothesis is a correct statement, what is the probability that the researcher will make the correct decision not to reject the null hypothesis? Answer: Given that The sample mean, x 75 a)The probability associated with mean of 75 (P-value is 0.05) Since the P-value is equal to the level of significance, do not reject the null hypothesis. b) If the null hypothesis is a correct statement, the probability that the researcher will make the correct decision not to reject the null hypothesis is nothing but 1-P(type I error) = 1 - 0.05 = 0.95